I too lived in Vienna for some time. I don't want to glorify this city further but focus on some of the museums found in the inscribed area - great works of art on their own right.

Belveder is a grand palace now housing the Austrian Gallery of Art. It mainly exhibits Austrian art with Oppenheimer, Schiele, Kokoschka and Klimt as its main gems. The Belveder is also quite impressive as a palace. Mainly its lesser palace has some beautiful chambers. There's also the lovely garden connecting the two palaces.

As its (for me unequal) rival (it is even better!) there is the Kunsthistorisches Museum (Museum of Art History) based on the Kaiser's art collections. Its exhibits are fantastic (especially Ancient Egypt, Rubens, Tizian and Breughel Elder). The building once again is a masterpiece built in a Neo-Baroque style but beautifully decorated in its interior by some Secession artists.

Another must-see on this list is the Secession building itself. It used to be the centre of Avant-Guard art at the end of the 19th Century. Except of Klimt's Beethoven Fries there isn't much of importance to see inside though, but the outside is a good exemplar of this school's revolutionary style.

In the Neues Palais (New Palace) of the royal residence you can see the Ephesos Collection (important findings from the now Turkish site), armoury, musical instruments and the royal treasury. All of these originally belonged to the royal family and are among the best of their kind in the world.